MinT - Best Known (94−83, 94, s)-Nets in Base 9

Best Known (94−83, 94, s)-Nets in Base 9

(94−83, 94, 40)-Net over F₉ — Constructive and digital

Digital (11, 94, 40)-net over F₉, using

t-expansion [i] based on digital (8, 94, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(94−83, 94, 55)-Net over F₉ — Digital

Digital (11, 94, 55)-net over F₉, using

net from sequence [i] based on digital (11, 54)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 11 and N(F) ≥ 55, using
  - a curve from the manYPoints database [i]

(94−83, 94, 105)-Net in Base 9 — Upper bound on s

There is no (11, 94, 106)-net in base 9, because

1 times m-reduction [i] would yield (11, 93, 106)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9⁹³, 106, S₉, 82), but
  - the linear programming bound shows that MÂ â‰¥ 59 420085 915766 107728 505751 844679 075927 724890 936316 820686 590430 232059 418945 034096 274957 873633 207402 099581 / 966 180894 535549 > 9⁹³ [i]